Swing plane is the vertical angle between the ground and the circle that the club head travels on during the bottom portion of the swing arc.
Swing plane is similar to what instructors refer to on video as “shaft plane”, but shaft plane uses a 2D camera image at one point (frame) in time.
Swing plane uses the three-dimensional position of the club head from approximately knee high to knee high on the downswing.
Shorter/higher lofted clubs generally result in a higher (more vertical) swing plane since the golf must stand closer to the ball and the plane the golfer swings on is typically more vertical with these shorter clubs. The swing plane number may closely resemble the lie angle of the golf club (e.g. 62 deg for a 7 iron, or 45-50 deg for a driver).
Swinging on plane is important because firstly we need to match the angle of the club we are using in order to apply force effectively. Secondly if the handle is too high or too low through impact this also means the clubface will open or close respectively (causing curvature in flight). Custom fitting lie angle can reduce this problem to some extent.